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Chabauty without the Mordell-Weil group

Title data

Stoll, Michael:
Chabauty without the Mordell-Weil group.
In: Böckle, Gebhard ; Decker, Wolfram ; Malle, Gunter (ed.): Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory. - Cham : Springer , 2017 . - pp. 623-663
ISBN 978-3-319-70565-1
DOI: https://doi.org/10.1007/978-3-319-70566-8_28

Project information

Project title:
Project's official titleProject's id
Algorithmic and Experimental Methods in Algebra, Geometry and Number TheorySPP 1489

Project financing: Deutsche Forschungsgemeinschaft

Abstract in another language

Based on ideas from recent joint work with Bjorn Poonen, we describe an algorithm that can in certain cases determine the set of rational points on a curve C, given only the p-Selmer group S of its Jacobian (or some other abelian variety C maps to) and the image of the p-Selmer set of C in S. The method is more likely to succeed when the genus is large, which is when it is usually rather difficult to obtain generators of a finite-index subgroup of the Mordell-Weil group, which one would need to apply Chabauty’s method in the usual way. We give some applications, for example to generalized Fermat equations of the form x^5 + y^5 = z^p.

Further data

Item Type: Article in a book
Refereed: Yes
Keywords: Rational points on curves; Chabauty’s method; Selmer group
Subject classification: Mathematics Subject Classification Code: 11G30 14G05 14G25 14H25 11Y50 11D41
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II > Chair Mathematics II - Univ.-Prof. Dr. Michael Stoll
Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 20 Jun 2018 11:29
Last Modified: 20 Jun 2018 11:29
URI: https://eref.uni-bayreuth.de/id/eprint/44579